Lecture20and21

Lecture20and21 - a e ie :h e a iab eC a e ig ea iab eca c h...

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Unformatted text preview: a e ie :h e a iab eC a e ig ea iab eca c h e ba ica ica i fh ed e ia i e i i h e c c i fa age i eF h eca c ff c i f a iab e h ec ed ig ih eage a e adb h age i ead age a ea ee feed a i ea ia i i ea a i a i A e eee i h eha f fh ic ehgh h eage i ecab e ie eda a i e a ia ha ih e d e e i h e i ee fec ie c e i d ceh ec ce fa a iab ea e ie ;h i a e ha ea d i a h e i ea a i a ib a h ead a ic a i a iad fc eah igh e d ea i a i h d ee e eed h ea e h d ek ha a a iab ea e ieh d k ik e? e e a ih ha ek ab h e ig ea iab ea ie !C id e a f c i f ( x, y ) ad eha e a aa i a i h i h ich i a id f a e f x ad y ea h e i ( x , y ) f eh ik f ea iab e a y a b e ig ed h e f ( x, y ) b ec ea f c i f x a ead eca ead i iaa e iece eeda x h e d iee ceb e ig ha h e d e ia i e f f eed b ee eeda a ia d e ia i e : f ( x, y ) = f ( x , y ) + f x ( x , y ) ( x- x ) + 1 2! f xx ( x , y ) ( x- x ) 2 + . . . h ee f ( x , y ) f x ( x , y ) f xx ( x , y ) e ca e fc e c a b d e ed h eecda iab e y h ee f e eh db eab e ead each fh e iaa e iece eeda y : f ( x , y ) = f ( x , y ) + f y ( x , y ) ( y- y ) + 1 2! f yy ( x , y ) ( y- y ) 2 + . . . f x ( x , y ) = f x ( x , y )+ f xy ( x , y ) ( y- y )+ 1 2! f xyy ( x , y ) ( y- y ) 2 + . . . f xx ( x , y ) = f xx ( x , y )+ f xxy ( x , y ) ( x- x )+ 1 2! f xxyy ( x , y ) ( y- y ) 2 + . . . 4 e c b i igeach fh ee i E a i d cea i iee ie fi ie e ie ! h id ie db if eh ikab ih e igh aae e ga c eb ec eaa e ea e ig c c...
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This note was uploaded on 04/05/2010 for the course MATH 119 taught by Professor Harmsworth during the Spring '08 term at Waterloo.

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Lecture20and21 - a e ie :h e a iab eC a e ig ea iab eca c h...

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